Camera resectioning is the process of estimating the parameters of a pinhole camera model approximating the camera that produced a given photograph or video. Usually, the pinhole camera parameters are represented in a 3 × 4 matrix called the camera matrix.
Contents
- Parameters of camera model
- Intrinsic parameters
- Extrinsic parameters
- Algorithms
- Zhangs method
- Derivation
- Tsais Algorithm
- Selbys method for X ray cameras
- References
This process is often called camera calibration, but "camera calibration" can also mean photometric camera calibration.
Parameters of camera model
Often, we use
Intrinsic parameters
The intrinsic matrix
Nonlinear intrinsic parameters such as lens distortion are also important although they cannot be included in the linear camera model described by the intrinsic parameter matrix. Many modern camera calibration algorithms estimate these intrinsic parameters as well in the form of non-linear optimisation techniques. This is done in the form of optimising the camera and distortion parameters in the form of what is generally known as bundle adjustment.
Extrinsic parameters
Camera calibration is often used as an early stage in computer vision.
When a camera is used, light from the environment is focused on an image plane and captured. This process reduces the dimensions of the data taken in by the camera from three to two (light from a 3D scene is stored on a 2D image). Each pixel on the image plane therefore corresponds to a shaft of light from the original scene. Camera resectioning determines which incoming light is associated with each pixel on the resulting image. In an ideal pinhole camera, a simple projection matrix is enough to do this. With more complex camera systems, errors resulting from misaligned lenses and deformations in their structures can result in more complex distortions in the final image. The camera projection matrix is derived from the intrinsic and extrinsic parameters of the camera, and is often represented by the series of transformations; e.g., a matrix of camera intrinsic parameters, a 3 × 3 rotation matrix, and a translation vector. The camera projection matrix can be used to associate points in a camera's image space with locations in 3D world space.
Camera resectioning is often used in the application of stereo vision where the camera projection matrices of two cameras are used to calculate the 3D world coordinates of a point viewed by both cameras.
Some people call this camera calibration, but many restrict the term camera calibration for the estimation of internal or intrinsic parameters only.
Algorithms
There are many different approaches to calculate the intrinsic and extrinsic parameters for a specific camera setup. The most common ones are:
- Direct linear transformation (DLT) method
- Zhang's method.
- Selby's method (for X-ray cameras)
Zhang's method
Zhang model is a camera calibration method that uses traditional calibration techniques (known calibration points) and self-calibration techniques (correspondence between the calibration points when they are in different positions). To perform a full calibration by the Zhang method at least three different images of the calibration target/gauge are required, either by moving the gauge or the camera itself. If some of the intrinsic parameters are given as data (orthogonality of the image or optical center coordinates) the number of images required can be reduced to two.
In a first step, an approximation of the estimated projection matrix
Derivation
Assume we have a homography
The circular points
We can actually ignore
Tsai's Algorithm
It is a 2-stage algorithm, calculating the pose (3D Orientation, and x-axis and y-axis translation) in first stage. In second stage it computes the focal length, distortion coefficients and the z-axis translation.
Selby's method (for X-ray cameras)
Selby's camera calibration method addresses the auto-calibration of X-ray camera systems. X-ray camera systems, consisting of the X-ray generating tube and a solid state detector can be modelled as pinhole camera systems, comprising 9 intrinsic and extrinsic camera parameters. Intensity based registration based on an arbitrary X-ray image and a reference model (as a tomographic dataset) can then be used to determine the relative camera parameters without the need of a special calibration body or any ground-truth data.